Waveguide couplers for multi-mode waveguides

ABSTRACT

An optical coupler includes a first waveguide including a first multi-mode waveguide section having a cross-section characterized by a first height and a first width that is greater than the first height and a second waveguide including a second multi-mode waveguide section having a cross-section characterized by a second height and a second width that is greater than the second height. The first multi-mode waveguide section is positioned adjacent to the second multi-mode waveguide section at least partially above or below the second multi-mode waveguide so that light entering the first multi-mode waveguide section is coupled from the first multi-mode waveguide section to the second multi-mode waveguide section. Methods for coupling light between waveguides with the optical coupler and optical devices that include the optical coupler are also described.

RELATED APPLICATIONS

This application is a divisional application U.S. patent applicationSer. No. 16/693,163, filed Nov. 22, 2019, which claims priority to U.S.Provisional Application No. 62/802,522, filed Feb. 7, 2019 and U.S.Provisional Application No. 62/776,936, filed Dec. 7, 2018, each ofwhich is incorporated herein by reference in its entirety.

TECHNICAL FIELD

This relates generally to waveguides, and more specifically to waveguidecouplers.

BACKGROUND

Optical waveguides are widely used for transmitting light. For example,optical fibers are used in various telecommunication systems. Slab orplanar waveguides are used in photonic devices for manipulating light(such as directing light, coupling light, filtering light, generatinglight output, etc.).

Although optical waveguides are generally known to have low loss intransmitting light, the loss can be significant in certain applications,such as long-haul communication. Some applications, such assingle-photon optics, cannot tolerate the loss in conventional opticalwaveguides, as devices with conventional optical waveguides would notoperate for such applications.

SUMMARY

In accordance with some embodiments, an optical coupler includes a firstwaveguide. The first waveguide includes a first multi-mode waveguidesection. The first multi-mode waveguide section has a cross-sectioncharacterized by a first height and a first width that is greater thanthe first height. The optical coupler also includes a second waveguidethat is distinct and separate from the first waveguide. The secondwaveguide includes a second multi-mode waveguide section that isdistinct and separate from the first multi-mode waveguide section. Thesecond multi-mode waveguide section has a cross-section characterized bya second height and a second width that is greater than the secondheight. The first multi-mode waveguide section is positioned adjacent tothe second multi-mode waveguide section at least partially above orbelow the second multi-mode waveguide so that light entering the firstmulti-mode waveguide section is coupled from the first multi-modewaveguide section to the second multi-mode waveguide section.

In some embodiments, the first multi-mode waveguide section and thesecond multi-mode waveguide section are configured to allow lightentering the first multi-mode waveguide section in a fundamental mode iscoupled from the first multi-mode waveguide section to the secondmulti-mode waveguide section while remaining in the fundamental mode.

In some embodiments, the first width is at least three times the firstheight; and the second width is at least three times the second height.

In some embodiments, a center-to-center distance between the firstmulti-mode waveguide section and the second multi-mode waveguide sectionis less than an average of the first width and the second width.

In some embodiments, the first waveguide includes a third multi-modewaveguide section that is distinct from, and mutually exclusive to, thefirst multi-mode waveguide section so that light propagating in thethird multi-mode waveguide section propagates toward the firstmulti-mode waveguide section. The second waveguide includes a fourthmulti-mode waveguide section that is distinct from, and mutuallyexclusive to, the second multi-mode waveguide section so that lightpropagating in the fourth multi-mode waveguide section propagates towardthe second multi-mode waveguide section.

In some embodiments, the first waveguide includes a fifth multi-modewaveguide section that is coupled to the first multi-mode waveguidesection on a first end and to the third multi-mode waveguide section ona second end that is opposite to the first end. The second waveguideincludes a sixth multi-mode waveguide section that is coupled to thesecond multi-mode waveguide section on a first end and to the fourthmulti-mode waveguide section on a second end that is opposite to thefirst end. At least one of the fifth multi-mode waveguide section andthe sixth multi-mode waveguide section is curved.

In some embodiments, the first waveguide includes a seventh multi-modewaveguide section that is distinct from, and mutually exclusive to, thefirst multi-mode waveguide section so that light propagating in thefirst multi-mode waveguide section propagates toward the seventhmulti-mode waveguide section. The second waveguide includes an eighthmulti-mode waveguide section that is distinct from, and mutuallyexclusive to, the second multi-mode waveguide section so that lightpropagating in the second multi-mode waveguide section propagates towardthe eighth multi-mode waveguide section.

In some embodiments, the first waveguide includes a ninth multi-modewaveguide section that is coupled to the first multi-mode waveguidesection on a first end and to the seventh multi-mode waveguide sectionon a second end that is opposite to the first end. The second waveguideincludes a tenth multi-mode waveguide section that is coupled to thesecond multi-mode waveguide section on a first end and to the eighthmulti-mode waveguide section on a second end that is opposite to thefirst end. At least one of the ninth multi-mode waveguide section andthe tenth multi-mode waveguide section is curved.

In some embodiments, the first waveguide includes a first single-modeinput waveguide section adiabatically coupled to the first multi-modewaveguide section so that the first multi-mode waveguide sectionreceives light from the first single-mode input waveguide section. Thesecond waveguide includes a second single-mode input waveguide sectionadiabatically coupled to the second multi-mode waveguide section so thatthe second multi-mode waveguide section receives light from the secondsingle-mode input waveguide section.

In some embodiments, the optical coupler further includes a firsttapered waveguide section, in the first waveguide, configured to enablethe adiabatic coupling of the first single-mode input waveguide sectionto the first multi-mode waveguide section; and a second taperedwaveguide section, in the second waveguide, configured to enable theadiabatic coupling of the second single-mode input waveguide section tothe second multi-mode waveguide section.

In some embodiments, the optical coupler includes, in the firstwaveguide: a first single-mode output waveguide section adiabaticallycoupled to the first multi-mode waveguide section so that the firstsingle-mode output waveguide section receives light from the firstmulti-mode waveguide section; and a third tapered waveguide sectionconfigured to enable the adiabatic coupling of the first multi-modewaveguide section to the first single-mode output waveguide section. Theoptical coupler also includes, in the second waveguide: a secondsingle-mode output waveguide section adiabatically coupled to the secondmulti-mode waveguide section so that the second single-mode outputwaveguide section receives light from the second multi-mode waveguidesection; and a fourth tapered waveguide section configured to enable theadiabatic coupling of the second multi-mode waveguide section to thesecond single-mode output waveguide section.

In some embodiments, the first multi-mode waveguide section and thesecond multi-mode waveguide section are parallel to each other; and thefirst multi-mode waveguide section and the second multi-mode waveguidesection are separated by a first edge-to-edge distance in an range of20-500 nm, e.g., between 50-300 nm.

In some embodiments, the first waveguide and the second waveguide arelocated over a substrate.

In some embodiments, the first waveguide and the second waveguide havesidewalls that are substantially perpendicular with respect to a surfaceof the substrate.

In some embodiments, the first multi-mode waveguide section is formed ina first layer of material located over the substrate; and the secondmulti-mode waveguide section is formed in a second layer of materiallocated over the substrate that is distinct and separate from the firstlayer of material.

In accordance with some embodiments, a method includes injecting firstlight into a first waveguide having a first multi-mode waveguidesection, the first multi-mode waveguide section having a cross-sectioncharacterized by a first height and a first width that is greater thanthe first height. The method also includes transferring at least aportion of the first light from the first multi-mode waveguide sectionto a second multi-mode waveguide section of a second waveguide that isdistinct and separate from the first waveguide and positioned at leastpartially above or below the first multi-mode waveguide section of thefirst waveguide, the second multi-mode waveguide section having across-section characterized by a second height and a second width thatis greater than the second height. The method further includespropagating the transferred portion of the first light.

In some embodiments, the first light propagates in the first waveguidein a fundamental mode; and the transferred portion of the first lightpropagates in the second waveguide in the fundamental mode.

In some embodiments, the first waveguide includes a single-mode inputwaveguide section adiabatically coupled with the first multi-modewaveguide section; and the method includes injecting the first lightinto the single-mode input waveguide section so that the first lightpropagates in the single-mode input waveguide section in the fundamentalmode and the first light is coupled to the first multi-mode waveguidesection while remaining in the fundamental mode.

In some embodiments, the method further includes injecting second lightinto the second waveguide; transferring at least a portion of the secondlight from the second multi-mode waveguide section to the firstmulti-mode waveguide section of the first waveguide; and propagating thetransferred portion of the second light through the first waveguide.

In accordance with some embodiments, an optical device includes a firstplurality of optical waveguides formed in a first layer of material; anda second plurality of optical waveguides formed in a second layer ofmaterial that is distinct and separate from the first layer of material.At least one optical waveguide of the first plurality of opticalwaveguides is coupled with an optical waveguide of the second pluralityof optical waveguides with any optical coupler described herein.

In accordance with some embodiments, a generalized Mach-Zehnderinterferometer includes a first multi-channel optical coupler with aplurality of output waveguides and a second multi-channel opticalcoupler with a plurality of input waveguides. At least one of the firstmulti-channel optical coupler and the second multi-channel opticalcoupler corresponds to one or a connected network of more than one ofany multi-mode optical coupler described herein. The generalizedMach-Zehnder interferometer also includes a plurality of opticalwaveguides, each optical waveguide coupled with a respective outputwaveguide of the first multi-channel optical coupler and a respectiveinput waveguide of the second multi-channel optical coupler; and one ormore phase shifters coupled with at least a subset of the plurality ofoptical waveguides.

In accordance with some embodiments, a multi-channel multi-mode opticalcoupler includes two or more multi-mode optical couplers. The two ormore multi-mode optical couplers includes a first multi-mode opticalcoupler. The first multi-mode optical coupler includes a first waveguideincluding a first multi-mode waveguide section and a second waveguidethat is distinct and separate from the first waveguide. The secondwaveguide includes a second multi-mode waveguide section. The firstwaveguide is located in a first layer of material, and the secondwaveguide is located in a second layer of material that is distinct andseparate from the first layer of material. The first multi-modewaveguide section is positioned adjacent to the second multi-modewaveguide section.

In some embodiments, the two or more multi-mode optical couplers alsoinclude a second multi-mode optical coupler. The second multi-modeoptical coupler includes a third waveguide including a third multi-modewaveguide section and a fourth waveguide that is distinct and separatefrom the third waveguide. The fourth waveguide including a fourthmulti-mode waveguide section. The fourth waveguide is located in thesecond layer of material, and the third waveguide being located in thefirst layer of material. The third multi-mode waveguide section ispositioned adjacent to the fourth multi-mode waveguide section. Aportion of the second waveguide is positioned adjacent to a portion ofthe third waveguide for coupling light from the second waveguide to thethird waveguide.

In some embodiments, the two or more multi-mode optical couplers alsoinclude a third multi-mode optical coupler and a fourth multi-modeoptical coupler. The third multi-mode optical coupler includes a fifthwaveguide including a fifth multi-mode waveguide section and the fourthwaveguide that is distinct and separate from the fifth waveguide. Thefifth waveguide being located in the first layer of material. The fourthwaveguide includes a sixth multi-mode waveguide section that isdifferent from the fourth multi-mode waveguide section. The fifthmulti-mode waveguide section is positioned adjacent to the sixthmulti-mode waveguide section. The fourth multi-mode optical couplerincludes the first waveguide including a seventh multi-mode waveguidesection that is different from the first multi-mode waveguide sectionand a sixth waveguide including an eighth multi-mode waveguide section.The sixth waveguide is located in the second layer of material. Theseventh multi-mode waveguide section is positioned adjacent to theeighth multi-mode waveguide section. A portion of the fifth waveguide ispositioned adjacent to a portion of the sixth waveguide for couplinglight from the fifth waveguide to the sixth waveguide.

In accordance with some embodiments, a generalized Mach-Zehnderinterferometer includes: a first multi-channel optical coupler thatincludes four or more output ports; a second multi-channel opticalcoupler that includes four or more input ports; and four or more opticalwaveguides. A respective optical waveguide of the four or more opticalwaveguides is connected to a respective output port of the four or moreoutput ports and a respective input port of the four or more inputports. The generalized Mach-Zehnder interferometer also includes one ormore phase shifters coupled with at least a subset of the four or moreoptical waveguides. At least one of the first multi-channel opticalcoupler and the second multi-channel optical coupler includes a firstwaveguide including a first multi-mode waveguide section and a secondwaveguide that is distinct and separate from the first waveguide. Thesecond waveguide includes a second multi-mode waveguide section. Thefirst multi-mode waveguide section is positioned adjacent to the secondmulti-mode waveguide section.

In some embodiments, the first waveguide is located in a first layer ofmaterial; and the second waveguide being located in a second layer ofmaterial that is distinct and separate from the first layer of material.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the various described embodiments,reference should be made to the Description of Embodiments below, inconjunction with the following drawings in which like reference numeralsrefer to corresponding parts throughout the figures.

FIGS. 1A and 1B are partial plan views of an optical coupler inaccordance with some embodiments.

FIGS. 1C, 1F, 1G and 1H are partial cross-sectional views of the opticalcoupler shown in FIGS. 1A and 1B.

FIGS. 1D and 1E are partial cross-sectional views of optical couplers inaccordance with some embodiments.

FIG. 2 is a partial plan view of an optical coupler in accordance withsome embodiments.

FIG. 3 is a perspective view of an optical coupler in accordance withsome embodiments.

FIG. 4 is a flowchart illustrating a method of transmitting lightthrough an optical coupler in accordance with some embodiments.

FIG. 5A is a schematic diagram illustrating a generalized Mach-Zehnderinterferometer in accordance with some embodiments.

FIG. 5B illustrates an example optical device, which corresponds to amulti-channel optical coupler shown in FIG. 5A.

These figures are not drawn to scale unless indicated otherwise.

DETAILED DESCRIPTION

As explained above, there is a need for optical waveguides with reducedloss. The above deficiencies and other problems associated withconventional optical waveguides are reduced or eliminated by thedisclosed optical waveguides. In slab or planar waveguides, some of thelosses occur when transmitted light comes into contact with walls thathave irregular surfaces. Planar waveguides fabricated with the currentlyavailable semiconductor fabrication techniques typically have top andbottom surfaces that are smoother than side walls (e.g., the surfaceroughness of the top and bottom surfaces is lower than the surfaceroughness of the side walls). The optical loss can decrease by reducinginteraction between light propagating within the optical waveguide andthe side walls. The disclosed embodiments include optical waveguidesthat are wide and short so that the distance between the side walls isgreater than the distance between the top and bottom surfaces. Thisconfiguration reduces the interaction between the transmitted light andthe side walls. In particular, when a fundamental mode is transmittedthrough the wide and short optical waveguide, the fundamental mode has awidth that extends less toward the side walls of the optical waveguide,compared to a fundamental mode transmitted through a single modewaveguide. This, in turn, reduces the loss of the transmitted light.

However, an optical coupler for such waveguides can have a lowercoupling efficiency for a given coupling length due to the increaseddistance between two waveguides when the two waveguides are placedside-by-side. Instead of increasing the coupling length to increase theoverall coupling efficiency of the optical coupler, which increases thesize of the optical coupler and also increases the attenuation withinthe optical coupler due to the increased coupling length, some of thedisclosed embodiments include waveguides that are located at leastpartially above or below each other so that the distance between the twowaveguides is reduced, which, in turn, allows a high coupling efficiencyfor the given coupling length.

Reference will now be made to embodiments, examples of which areillustrated in the accompanying drawings. In the following description,numerous specific details are set forth in order to provide anunderstanding of the various described embodiments. However, it will beapparent to one of ordinary skill in the art that the various describedembodiments may be practiced without these specific details. In otherinstances, well-known methods, procedures, components, circuits, andnetworks have not been described in detail so as not to unnecessarilyobscure aspects of the embodiments.

It will also be understood that, although the terms first, second, etc.are, in some instances, used herein to describe various elements, theseelements should not be limited by these terms. These terms are used onlyto distinguish one element from another. For example, a first waveguidecould be termed a second waveguide, and, similarly, a second waveguidecould be termed a first waveguide, without departing from the scope ofthe various described embodiments. The first waveguide and the secondwaveguide are both waveguides, but they are not the same waveguide.

The terminology used in the description of the various embodimentsdescribed herein is for the purpose of describing particular embodimentsonly and is not intended to be limiting. As used in the description ofthe various described embodiments and the appended claims, the singularforms “a,” “an,” and “the” are intended to include the plural forms aswell, unless the context clearly indicates otherwise. It will also beunderstood that the term “and/or” as used herein refers to andencompasses any and all possible combinations of one or more of theassociated listed items. It will be further understood that the terms“includes,” “including,” “comprises,” and/or “comprising,” when used inthis specification, specify the presence of stated features, integers,steps, operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, integers, steps,operations, elements, components, and/or groups thereof. The term“exemplary” is used herein in the sense of “serving as an example,instance, or illustration” and not in the sense of “representing thebest of its kind.”

FIGS. 1A and 1B are partial plan views of an optical coupler 100 forcoupling light between waveguides in accordance with some embodiments.

The optical coupler 100 includes a first waveguide 150 and a secondwaveguide 152 that is distinct and separate from the first waveguide150. The first waveguide 150 includes a first multi-mode waveguidesection 160-A between lines 102-1 and 102-2 (representing the couplingregion). The second waveguide 152 includes, between lines 102-1 and102-2, a second multi-mode waveguide section 170-A that is distinct andseparate from the first multi-mode waveguide section 160-A. In someembodiments, the length of the first and/or second multi-mode waveguidesections 160-A and 170-A (i.e., the distance between lines 102-1 and102-2) is between 5-200 μm but other lengths are possible withoutdeparting from the scope of the present disclosure.

A coupling efficiency between the first waveguide 150 and the secondwaveguide 152 is determined based on the length of the first and secondmulti-mode waveguide sections 160-A and 170-A, in addition to therefractive index of the first waveguide 150, the refractive index of thesecond waveguide 152, the width and height of the first waveguide 150,the width and height of the second waveguide 152, the refractive indexof the material located between the first waveguide 150 and the secondwaveguide 152, and the distance between the first waveguide 150 and thesecond waveguide 152. In some embodiments, at least one of the length ofthe first multi-mode waveguide section 160-A and the length of thesecond multi-mode waveguide section 170-A corresponds to 100% couplingefficiency between the first waveguide 150 and the second waveguide 152(for a given set of parameters for the refractive index of the firstwaveguide 150, the refractive index of the second waveguide 152, thewidth and height of the first waveguide 150, the width and height of thesecond waveguide 152, the refractive index of the material locatedbetween the first waveguide 150 and the second waveguide 152, and thedistance between the first waveguide 150 and the second waveguide 152).In some embodiments, at least one of the length of the first multi-modewaveguide section 160-A and the length of the second multi-modewaveguide section 170-A corresponds to a coupling efficiency between thefirst waveguide 150 and the second waveguide 152 that is less than 100%(e.g., between 1% and 99%, between 10% and 90%, between 20% and 80%,between 30% and 70%, between 40% and 60%, between 45% and 55%, andbetween 49% and 51%, etc.). For example, the optical coupler 100 having50% coupling efficiency may operate as a 50/50 beam splitter.

In some embodiments, the first multi-mode waveguide section 160-A is astraight waveguide section. In some embodiments, the second multi-modewaveguide section 170-A is a straight waveguide section.

In some embodiments, the first multi-mode waveguide section 160-A andthe second multi-mode waveguide section 170-A are parallel to eachother.

In some embodiments, the first waveguide 150 and the second waveguide152 are made of the same material (e.g., silicon, silicon nitride,silicon oxynitride, indium phosphide, gallium arsenide, aluminum galliumarsenide, lithium niobite, or any other suitable photonic materialincluding silicon and/or germanium based materials). In someembodiments, the first waveguide 150 and the second waveguide 152 aremade of different materials (e.g., the first waveguide 150 is made ofsilicon and the second waveguide 152 is made of silicon nitride).

Also shown in FIG. 1A are a third multi-mode waveguide section 160-B anda fourth multi-mode waveguide section 170-B. The third multi-modewaveguide section 160-B is coupled to the first multi-mode waveguidesection 160-A via a fifth multi-mode waveguide section 160-C locatedbetween lines 102-3 and 102-1, and the fourth multi-mode waveguidesection 170-B is coupled to the second multi-mode waveguide section170-A via a sixth multi-mode waveguide section 170-C between lines 102-4and 102-1. In some embodiments, the fifth multi-mode waveguide section160-C is curved as shown in FIG. 1A. In some embodiments, the fifthmulti-mode waveguide section 160-C is straight. In some embodiments, thesixth multi-mode waveguide section 170-C is curved as shown in FIG. 1A.In some embodiments, the sixth multi-mode waveguide section 170-C isstraight. In some embodiments, at least one of the fifth multi-modewaveguide section 160-C and the sixth multi-mode waveguide section 170-Chas a portion that is curved.

FIG. 1A also shows a seventh multi-mode waveguide section 160-D and aneighth multi-mode waveguide section 170-D. The seventh multi-modewaveguide section 160-D is coupled to the first multi-mode waveguidesection 160-A via a ninth multi-mode waveguide section 160-E locatedbetween lines 102-2 and 102-5, and the eighth multi-mode waveguidesection 170-D is coupled to the second multi-mode waveguide section170-A via a tenth multi-mode waveguide section 170-E between lines 102-2and 102-6. In some embodiments, the ninth multi-mode waveguide section160-E is curved as shown in FIG. 1A. In some embodiments, the ninthmulti-mode waveguide section 160-E is straight. In some embodiments, thetenth multi-mode waveguide section 170-E is curved as shown in FIG. 1A.In some embodiments, the tenth multi-mode waveguide section 170-E isstraight. In some embodiments, at least one of the ninth multi-modewaveguide section 160-E and the tenth multi-mode waveguide section 170-Ehas a portion that is curved.

In some embodiments, a waveguide section of waveguide sections 160-C,170-C, 160-E, and 170-E includes two or more curved sections (e.g., anyof waveguide sections 160-C, 170-C, 160-E, and 170-E can have two ormore curved sections having different centers of curvature, such ascurved sections forming an s-curve). In some embodiments, the specificshape of the curves is designed to ensure adiabaticity of the opticalmode of light as the light travels through the curved portion (e.g.,light launched into the first curve in the fundamental mode will largelyremain in the fundamental mode while propagating through the curves). Asone of ordinary skill in the art would appreciate, the requirement foradiabaticity ensures that the excitation of higher order modes isreduced, e.g., excitation of higher order transverse modes, backscattered modes, and/or radiative modes, is minimized as the lighttravels through the curved sections. Depending on the geometricconstraints of the device layout, any number of different types ofcurves can be used including, e.g., Euler bends, Bezier curves, S-curvesand the like. Furthermore, the specific geometry that satisfies theadiabaticity condition will depend on the index of refraction around thewaveguide itself. Thus, the curve shape at the input portion (e.g., thecurve of a portion of the waveguide section 160-C proximate to line102-3) may be different from the curve at the output portion (e.g., thecurve of a portion of the waveguide section 160-C proximate to thecoupling region, just before the line 102-1). These curves may bedifferent because the presence of the other waveguide just above or justbelow may affect the local refractive index near the bend and therebychange the adiabaticity condition in that region.

As shown in FIG. 1A, when light 110 is injected into the thirdmulti-mode waveguide section 160-B of the first waveguide 150, the light110 propagates toward the fifth multi-mode waveguide section 160-C andenters the first multi-mode waveguide section 160-A, where the light 110is coupled to the second multi-mode waveguide section 170-A.Subsequently, the light 110 propagates within the second waveguide 152from the second multi-mode waveguide section 170-A through the tenthmulti-mode waveguide section 170-E toward the eighth multi-modewaveguide section 170-D.

Additionally or alternatively, when light 112 is injected into thefourth multi-mode waveguide section 170-B of the second waveguide 152,the light 112 propagates toward the sixth multi-mode waveguide section170-C and enters the second multi-mode waveguide section 170-A, wherethe light 112 is coupled to the first multi-mode waveguide section160-A. Subsequently, the light 112 propagates within the first waveguide150 from the first multi-mode waveguide section 160-A through the ninthmulti-mode waveguide section 160-E toward the seventh multi-modewaveguide section 160-D.

Turning to FIG. 1B, line AA′ represents a view from which thecross-section shown in FIG. 1C is taken, line BB′ represents a view fromwhich the cross-section shown in FIG. 1F is taken, line CC′ represents aview from which the cross-section shown in FIG. 1G is taken, and lineDD′ represents a view from which the cross-section shown in FIG. 1H istaken.

FIG. 1C shows that the first multi-mode waveguide section 160-A has across-section characterized by first height h1 (also called a firstthickness) and first width w1 that is greater than the first height h1.

FIG. 1C also shows that the second multi-mode waveguide section 170-Ahas a cross-section characterized by second height h2 (also called asecond thickness) and a second width w2 that is greater than the secondheight h2.

In some embodiments, the heights h1 and h2 and the widths w1 and w2 arechosen to reduce or minimize loss. For example, in some embodiments, theside walls (e.g., side walls 166 and 176) of the waveguides may berougher than the top and bottom surfaces (e.g., top and bottom surfaces165, 167, 175 and 177) of the waveguides. In such a case, a large widthwaveguide will be beneficial because for larger waveguide widths, thefraction of the fundamental mode that extends out of the waveguide isreduced. Accordingly, for larger waveguide widths, there is a lowerprobability of exciting higher order modes (such as radiative modes orback reflective modes) due to the interaction of the optical mode withthe rough sidewalls. In such a case, if the top and bottom walls aresmooth, then the thickness of the waveguide can be smaller than thewidth of the waveguide. On the other hand, if both the sidewalls and thetop and bottom surfaces are rough, it may be beneficial to have a largewidth and a large thickness. Likewise, if the top and bottom surfacesare rough but the sidewalls are smooth, it may be beneficial to have awaveguide whose thickness exceeds its width.

In some embodiments (e.g., where the sidewall roughness is the dominantsource of scattering and loss), a respective multi-mode waveguidesection (e.g., the first multi-mode waveguide section 160-A and/or thesecond multi-mode waveguide section 170-A) has a width between 0.5 μm-10μm. In some embodiments, the respective multi-mode waveguide section hasa height between 20 nm-1 μm. Accordingly, in this example, the waveguidewidth can range from approximately 3 to 10 times the waveguidethickness. Likewise, if the roughness of the top and bottom surfaces ofthe waveguide are greater than the roughness of the sidewalls, then thewaveguide thickness can range from approximately 3 to 10 times thethickness, which could be represented pictorially as the waveguidesshown in FIG. 1C being rotated 90 degrees about an axis that extendsperpendicularly out of the page.

In some embodiments, the first width w1 corresponds to the second widthw2 (e.g., FIG. 1C). In some embodiments, the first width w1 is differentfrom the second width w2 (e.g., the first width w1′ in FIG. 1D is lessthan the second width w2). In some embodiments, the first height h1corresponds to the second height h2 (e.g., FIG. 1C). In someembodiments, the first height h1 is different from the second height h2(e.g., the first height h1 is less than the second height h2). Forexample, when the first multi-mode waveguide section 160-A and thesecond multi-mode waveguide section 170-A are made of differentmaterials, the size (e.g., the height and/or the width) of at least oneof the two multi-mode waveguide sections 160-A and 170-A is adjusted forimpedance matching between the two multi-mode waveguide sections 160-Aand 170-A.

The first multi-mode waveguide section 160-A is positioned at leastpartially above or below the second multi-mode waveguide section 170-A.In some cases, the entire width of the first multi-mode waveguidesection 160-A is located above the second multi-mode waveguide section170-A as shown in FIG. 1C. In some cases, the first multi-mode waveguidesection 160-A is partially offset from the second multi-mode waveguidesection 170-A (e.g., only a portion of the first multi-mode waveguidesection 160-A is located directly above the second multi-mode waveguidesection 170-A and another portion of the first multi-mode waveguidesection 160-A is not located directly above the second multi-modewaveguide section 170-A as shown in FIG. 1E).

Turning back to FIG. 1C, the first multi-mode waveguide section 160-Aand the second multi-mode waveguide section 170-A are configured toallow light entering the first multi-mode waveguide section 160-A to becoupled from the first multi-mode waveguide section 160-A to the secondmulti-mode waveguide section 170-A. In particular, the first multi-modewaveguide section 160-A and the second multi-mode waveguide section170-A are configured to allow light entering the first multi-modewaveguide section 160-A in a fundamental mode to be coupled from thefirst multi-mode waveguide section 160-A to the second multi-modewaveguide section 170-A while the coupled light remains in thefundamental mode. For example, the first multi-mode waveguide section160-A has a first distance 140 to the second multi-mode waveguidesection 170-A that allows optical coupling from the first multi-modewaveguide section 160-A to the second multi-mode waveguide section170-A. In some embodiments, the first distance 140 is between 20 nm-500nm. For example, as shown in FIG. 1H, light entering the firstmulti-mode waveguide section 160-A from a section 160-E is transmittedto the second multi-mode waveguide section 170-A, for example viaevanescent coupling, and light entering the second multi-mode waveguidesection 170-A from a section 170-E is transmitted to the firstmulti-mode waveguide section 160-A, for example via evanescent coupling.

For some of the configurations in which the first multi-mode waveguidesection 160-A and the second multi-mode waveguide section 170-A are notlocated side-by-side, a center-to-center distance between the firstmulti-mode waveguide section 160-A and the second multi-mode waveguidesection 170-A is less than an average of the first width w1 and thesecond width w. In comparison, for a configuration in which the firstmulti-mode waveguide section and the second multi-mode waveguide sectionis located side-by-side, the center-to-center distance between the firstmulti-mode waveguide section and the second multi-mode waveguide sectionis greater than the average of the first width and the second width(i.e., the sum of a half-width of the first multi-mode waveguide sectionand a half-width of the second multi-mode waveguide section). Byreducing the center-to-center distance between the first multi-modewaveguide section and the second multi-mode waveguide section, thecoupling efficiency between the two multi-mode waveguide sections thatare located above and below each other is increased, compared to thecoupling efficiency between two multi-mode waveguide sections that arelocated side-by-side.

In some embodiments, the first waveguide 150 and the second waveguide152 are located over a substrate 190. In some embodiments, the substrate190 is a semiconductor substrate (e.g., a silicon substrate).

In some embodiments, the first waveguide 150 and the second waveguide152 have sidewalls 166 and 176 that are substantially perpendicular withrespect to a surface 191 of the substrate 190 (e.g., each of thesidewalls 166 and 176 forms an angle between 85 degrees and 95 degreeswith the top surface 191 and/or the bottom surface of the substrate190). In other embodiments, the sidewalls are not perpendicular andcould be positioned at an angle relative to the top and bottom surfaces,e.g., forming a waveguide having a trapezoidal shape (e.g., atrapezoidal cross-section).

In some embodiments, the first multi-mode waveguide section 160-A isformed in a first layer 197 of material located over the substrate 190,and the second multi-mode waveguide section 170-A is formed in a secondlayer 199 of material located over the substrate 190 that is distinctand separate from the first layer of material.

In some embodiments, the first layer of material and the second layer ofmaterial are separated by a third layer of material that is distinctfrom the first layer 197 of material and the second layer 199 ofmaterial (e.g., the third layer 198 of material has a chemicalcomposition that is different from the chemical composition of thematerial in the first layer and the second layer). For example, in somecases, the first layer 197 of material and the second layer 199 ofmaterial are made of silicon (e.g., the first layer 197 and the secondlayer 199 consist of silicon), and the third layer 198 of material ismade of silicon oxide (e.g., the third layer 198 consists of siliconoxide, also known as silicon dioxide). In some embodiments, the firstlayer 197 and the second layer 199 can be different materials, e.g., onecan be formed of Si and one from SiN.

In some embodiments, the first multi-mode waveguide section 160-A andthe second multi-mode waveguide section 170-A are covered by aprotective layer 130. In some embodiments, the protective layer 130 ismade of the same material that constitutes the third layer 198. In someembodiments, the protective layer 130 is made of a material that isdifferent from the material constituting the third layer 198.

Returning to FIG. 1A, the third multi-mode waveguide section 160-B has afirst lateral distance 142, greater than the first distance 140, to thefourth multi-mode waveguide section 170-B. As shown in FIG. 1F, thefirst lateral distance 142 is a center-to-center distance between thethird multi-mode waveguide section 160-B and the fourth multi-modewaveguide section 170-B on a plane that is parallel to the surface 191of the substrate 190. In some embodiments, the first lateral distance142 is at least 1 μm, but one of ordinary skill in the art willappreciate that this lateral distance depends on many factors includingthe waveguide width, curve design, index of refraction of the waveguidecore and surrounding material, etc. The first lateral distance 142between the third multi-mode waveguide section 160-B and the fourthmulti-mode waveguide section 170-B is significantly greater than thefirst distance 140 between the first multi-mode waveguide section 160-Aand the second multi-mode waveguide section 160-B. As a result, lightdoes not couple between the third multi-mode waveguide section 160-B andthe fourth multi-mode waveguide section 170-B.

Returning to FIG. 1A, the seventh multi-mode waveguide section 160-D hasa second lateral distance 144, greater than the first distance 140, tothe eighth multi-mode waveguide section 170-D. As shown in FIG. 1G, thesecond lateral distance 144 is a center-to-center distance between theseventh multi-mode waveguide section 160-D and the eighth multi-modewaveguide section 170-D on a plane that is parallel to the surface 191of the substrate 190. In some embodiments, the second lateral distance144 between the seventh multi-mode waveguide section 160-D and theeighth multi-mode waveguide section 170-D is identical to the firstlateral distance 142 between the third multi-mode waveguide section160-B and the fourth multi-mode waveguide section 170-B. In someembodiments, the second lateral distance 144 between the seventhmulti-mode waveguide section 160-D and the eighth multi-mode waveguidesection 170-D is different from the first lateral distance 142 betweenthe third multi-mode waveguide section 160-B and the fourth multi-modewaveguide section 170-B.

In some embodiments, at least one of the ninth multi-mode waveguidesection 160-E and the tenth multi-mode waveguide section 170-E has aportion that is curved to ensure adiabatic propagation of thefundamental waveguide mode as described above in reference to FIG. 1A.

FIG. 1H includes a schematic diagram illustrating the transfer of atleast a portion of the first light from the first multi-mode waveguidesection 160-A of the first waveguide 150 to the second multi-modewaveguide section 170-A of the second waveguide 152 (e.g., viaevanescent coupling). Typically, the amount of the first light that istransferred from the first multi-mode waveguide section 160-A to thesecond multi-mode waveguide section 170-A is determined based on thematerial of the first multi-mode waveguide section 160-A, the materialof the second multi-mode waveguide section 170-A, the material locatedbetween the first multi-mode waveguide section 160-A and the secondmulti-mode waveguide section 170-A, the distance between the firstmulti-mode waveguide section 160-A and the second multi-mode waveguidesection 170-A, the size (e.g., the width and the height) of the firstmulti-mode waveguide section 160-A, the size (e.g., the width and theheight) of the second multi-mode waveguide section 170-A, the length ofthe coupling region (e.g., a length of the first multi-mode waveguidesection 160-A and/or a length of the second multi-mode waveguide section170-A), and the wavelength of the transferred light.

In some embodiments, the entire first light is transferred from thefirst multi-mode waveguide section 160-A to the second multi-modewaveguide section 170-A. In some embodiments, less than all of the lightis transferred from the first multi-mode waveguide section 160-A to thesecond multi-mode waveguide section 170-A. Advantageously, in someembodiments the minimum length of the multi-mode waveguide sections160-A and 170-A (also referred to herein as the interaction region) toachieve maximum coupling between the waveguides for a given separationbetween the waveguides can be smaller than the minimum length of theinteraction region for an architecture that places both multimodewaveguides adjacent to each other on a single layer. This is due to thefact that in a multi-layer configuration (i.e., stacked configuration)the centroids of the optical modes can be placed closer to each otherthan in a side-by-side configuration, especially when the width of themulti-mode waveguides is large (as is desired to achieve low loss). Asnoted already in reference to FIGS. 1A-1G, in some embodiments, thelength of the interaction region can be in a range of 5-200 μm, and forsome designs, can be as small as 5 μm, between 5-10 μm, between 5-20 μm,between 5-30 μm, between 5-40 μm, between 5-50 μm, between 5-60 μm,between 5-70 μm, between 5-80 μm, between 5-90 μm, between 5-100 μm,between 5-110 μm, between 5-120 μm, between 5-130 μm, between 5-140 μm,between 5-150 μm, between 5-160 μm, between 5-170 μm, between 5-180 μm,between 5-190 μm, and between 5-200 μm, even assuming relatively widemultimode waveguides, e.g., having widths between 0.5 μm-10 μm andassuming a silicon on insulator photonic platform.

FIG. 2 is a partial plan view of an optical coupler 200 in accordancewith some embodiments. The optical coupler 200 is similar to the opticalcoupler 100 shown in FIGS. 1A-1H. However, in some embodiments, theoptical coupler 200 differs from the optical coupler 100 at least inthat that the first waveguide 150 includes a first single-mode inputwaveguide section 164 adiabatically coupled to the first multi-modewaveguide section 160-A and configured to provide light to the firstmulti-mode waveguide section 160-A (e.g., through the third multi-modewaveguide section 160-B and the fifth multi-mode waveguide section160-C) and a second single-mode input waveguide section 174adiabatically coupled to the second multi-mode waveguide section 170-Aand configured to provide light to the second multi-mode waveguidesection 170-A (e.g., through the fourth multi-mode waveguide section170-B and the sixth multi-mode waveguide section 170-C).

In some embodiments, the optical coupler 200 also includes a firsttapered waveguide section 180, in the first waveguide 150, configured toenable the adiabatic coupling of the first multi-mode waveguide section160-A to the first single-mode input waveguide section 164 (e.g.,through the fifth multi-mode waveguide section 160-C and the thirdmulti-mode waveguide section 160-B). The optical coupler 200 alsoincludes a second tapered waveguide section 182, in the second waveguide152, configured to enable the adiabatic coupling of the secondmulti-mode waveguide section 170-A to the second single-mode inputwaveguide section 174 (e.g., through the sixth multi-mode waveguidesection 170-C and the fourth multi-mode waveguide section 170-B). Asdiscussed above with respect to FIG. 1A, the term adiabatic refers to anoptical element (e.g., a coupler or taper or a bend) that has theproperty that as the fundamental mode propagates through the opticalelement, the excitation of higher order modes, radiative modes, backreflection modes, etc. are reduced or suppressed, thereby reducingoptical loss.

In some embodiments, the width of each tapered section gradually andcontinuously varies form a first width (e.g., a width of the thirdmulti-mode waveguide section 160-B) to a second width (e.g., a width ofthe first single-mode waveguide section 162). For example, the totallength of the transition region could be between 10 μm-500 μm.

In some embodiments, the optical coupler 200 includes, in the firstwaveguide 150, a first single-mode output waveguide section 162adiabatically coupled to the first multi-mode waveguide section 160-A(e.g., through the seventh multi-mode waveguide section 160-D and theninth multi-mode waveguide section 160-E) so that the first multi-modewaveguide section 160-A is configured to provide light to the firstsingle-mode output waveguide section 162. The optical coupler 200 alsoincludes a third tapered waveguide section 184 configured to enable theadiabatic coupling of the first single-mode output waveguide section 162to the first multi-mode waveguide section 160-A (e.g., through theseventh multi-mode waveguide section 160-D and the ninth multi-modewaveguide section 160-E).

In some embodiments, the optical coupler 200 includes, in the secondwaveguide 152, a second single-mode output waveguide section 172adiabatically coupled to the second multi-mode waveguide section 170-A(e.g., through the eighth multi-mode waveguide section 170-D and thetenth multi-mode waveguide section 170-E) so that the second multi-modewaveguide section 170-A is configured to provide light to the secondsingle-mode output waveguide section 172. The optical coupler 200 alsoincludes a fourth tapered waveguide section 186 configured to enable theadiabatic coupling of the second single-mode output waveguide section172 to the second multi-mode waveguide section 170-A (e.g., through theeighth multi-mode waveguide section 170-D and the tenth multi-modewaveguide section 170-E).

In some embodiments, the first single-mode input waveguide section 164is configured to change a direction of light before the light isadiabatically coupled to the first multi-mode waveguide section 160-A(e.g., the first single-mode input waveguide section is curved). In someembodiments, the second single-mode input waveguide section 174 isconfigured to change a direction of light before the light isadiabatically coupled to the second multi-mode waveguide section 170-A(e.g., the second single-mode input waveguide section is curved).

In some embodiments, the first single-mode output waveguide section 162is configured to change a direction of light after the light isadiabatically coupled from the first multi-mode waveguide section 160-A(e.g., the first single-mode output waveguide section is curved). Insome embodiments, the second single-mode output waveguide section 172 isconfigured to change a direction of light after the light isadiabatically coupled form the second multi-mode waveguide section 170-A(e.g., the second single-mode output waveguide section is curved).

In some embodiments, a respective single-mode waveguide section (e.g.,the first single-mode input waveguide section 164, the secondsingle-mode input waveguide section 174, the first single-mode outputwaveguide section 162, and the second single-mode output waveguidesection 172) has a width between 150 nm and 600 nm. In some embodiments,a respective single-mode waveguide section has a height between 100 nmand 300 nm. In some cases, the respective single-mode waveguide sectionhas a width of 400 nm and a height of 200 nm. One of ordinary skill willappreciate that the above numbers apply to devices fabricated by asilicon on insulator (SOI) photonic process and that many other widthsand heights are possible depending on the choice of material and/orfabrication process.

FIG. 3 is a perspective view of an optical coupler 300 in accordancewith some embodiments.

The optical coupler 300 includes a first multi-mode waveguide section302 that has a cross-section characterized by a first height and a firstwidth that is greater than the first height (e.g., the first multi-modewaveguide section 302 is wider than its height).

The optical coupler 300 also includes a second waveguide section 304that is distinct and separate from the first waveguide section 302. Thesecond waveguide 304 has a cross-section characterized by a secondheight and a second width that is greater than the second height (e.g.,the second multi-mode waveguide section 304 is wider than its height).

The first multi-mode waveguide section 302 is positioned adjacent to thesecond multi-mode waveguide section 304 at least partially above orbelow the second multi-mode waveguide 304 and has a first distance tothe second multi-mode waveguide section 304 so that light entering thefirst multi-mode waveguide section 302 is coupled from the firstmulti-mode waveguide section 302 to the second multi-mode waveguidesection 304 and/or light entering the second multi-mode waveguidesection 304 is coupled from the second multi-mode waveguide section 304to the first multi-mode waveguide section 302.

The optical coupler 300 is similar to the optical coupler 100 shown inFIGS. 1A-1H, except that a first end 312 of the first multi-modewaveguide section 302 is not connected to another waveguide section (asa result, a portion of light transmitted through the first waveguide butnot coupled to the second waveguide ceases to propagate along the firstwaveguide at the first end 312 of the first multi-mode waveguide section302) while a first end 314 of the second multi-mode waveguide section304 is connected to another waveguide section 334 (as a result, thelight transferred from the first multi-mode waveguide section 302 to thesecond multi-mode waveguide section 304 continues to propagate throughthe second waveguide). In addition, a second end 322 of the firstmulti-mode waveguide section 302, opposite to the first end 312 of themulti-mode waveguide section 302, is connected to another waveguidesection 332 (e.g., as a result, the first multi-mode waveguide section302 receives light from the waveguide section 332 prior to transferringthe light to the second multi-mode waveguide section 304 through opticalcoupling) while a second end 324 of the second multi-mode waveguidesection 304, opposite to the first end 314 of the second multi-modewaveguide section 304, is not connected to another waveguide section (asa result, the second waveguide receives light primarily from the firstwaveguide through the optical coupling).

FIG. 4 is a flowchart illustrating a method 400 of transmitting lightbetween waveguides in accordance with some embodiments.

The method 400 includes (402) injecting first light into a firstwaveguide 150 having a first multi-mode waveguide section 160-A (e.g.,injecting light having a wavelength Xi into the seventh multi-modewaveguide section 160-D of the first waveguide 150 as shown in FIG. 1B).The first multi-mode waveguide section 160-A has a cross-sectioncharacterized by first height h1 and first width w1 that is greater thanthe first height h1 (FIG. 1C).

In some embodiments, the first waveguide includes (404) a single-modeinput waveguide section adiabatically coupled with the first multi-modewaveguide section (e.g., the single-mode input waveguide section 164 inFIG. 2 ). The method includes injecting the first light into thesingle-mode input waveguide section so that the first light propagatesin the single-mode input waveguide section in the fundamental mode andthe first light is coupled to the first multi-mode waveguide sectionwhile remaining in the fundamental mode.

The method 400 also includes (406) transferring at least a portion ofthe first light from the first multi-mode waveguide section 160-A to asecond multi-mode waveguide section 170-A of a second waveguide 152 thatis distinct and separate from the first waveguide 150 and positioned atleast partially above or below the first multi-mode waveguide section160-A of the first waveguide 150 (e.g., FIGS. 1B and 1E). The secondmulti-mode waveguide section 170-A has a cross-section characterized bysecond height h2 and a second width 192 that is greater than the secondheight h2 (FIG. 1C).

The method 400 further includes (408) propagating the transferredportion of the first light through the second waveguide 152 (e.g., thelight having the wavelength λ₁ propagates through the fourth multi-modewaveguide section 170-B of the second waveguide 152 as shown in FIG.1B).

In some embodiments, the first light propagates (410) in the firstwaveguide in a fundamental mode; and the transferred portion of thefirst light propagates in the second waveguide in the fundamental mode.Due to the shape of the first multi-mode waveguide section, the firstlight propagating in the fundamental mode within the first multi-modewaveguide section has a reduced interaction with the side walls of thefirst multi-mode waveguide section, which, in turn, reduces the loss ofthe first light while the first light propagates within the firstmulti-mode waveguide section. Similarly, due to the shape of the secondmulti-mode waveguide section, the transmitted portion of the first lightpropagating in the fundamental mode within the second multi-modewaveguide section has a reduced interaction with the side walls of thesecond multi-mode waveguide section, which, in turn, reduces the loss ofthe transmitted portion of the first light while the transmitted portionof the first light propagates within the second multi-mode waveguidesection.

In some embodiments, the method includes (412) injecting second lightinto the second waveguide (e.g., injecting light having a wavelength λ₂into the eighth multi-mode waveguide section 170-D of the secondwaveguide 152 as shown in FIG. 1B); transferring at least a portion ofthe second light from the second multi-mode waveguide section 170-A tothe first multi-mode waveguide section 160-A of the first waveguide 150;and propagating the transferred portion of the second light through thefirst waveguide 150 (e.g., the light having the wavelength λ₂ propagatesthrough the third multi-mode waveguide section 160-B of the firstwaveguide 150 as shown in FIG. 1B).

In some embodiments, the first light and the second light are infraredlight. In some embodiments, the first light and the second light have acenter wavelength between 300 nm and 3000 nm (e.g., between 1400 nm and1700 nm) depending on the choice of material. In some embodiments, thefirst light has a first center wavelength and the second light has asecond center wavelength distinct from the first center wavelength.

In some embodiments, the first waveguide and the second waveguide haveone or more features described with respect to FIGS. 1A-1H and 2-3 . Forexample, at least one of the first waveguide and the second waveguideincludes a curved multi-mode waveguide section. For brevity, suchdetails are not repeated herein.

FIG. 5A is a schematic diagram illustrating a generalized Mach-Zehnderinterferometer in accordance with some embodiments. The generalizedMach-Zehnder interferometer includes multi-channel optical couplers502-1 and 502-2 coupled with multiple waveguides. As described withrespect to FIG. 5B, at least one of the multi-channel optical couplers502-1 and 502-2 includes a multi-mode optical coupler described above.

The generalized Mach-Zehnder interferometer also includes a plurality ofphase shifters 504 coupled with at least a subset of the multiplewaveguides between the multi-channel optical couplers 502-1 and 502-2. Aphase shifter is configured to change a phase of light propagatingthrough an associated waveguide. For example, a phase shifter changes atemperature of a material forming the waveguide, which, in turn, changesa refractive index of the material and the phase of light propagatingwithin the waveguide. Alternatively, or in addition, the phase shifterchanges the refractive index of the material by applying an electricfield.

The generalized Mach-Zehnder interferometer is sometimes used as anoptical switch or a power splitter. For example, a generalizedMach-Zehnder interferometer can be used to receive light from one ormore input waveguides and relay the light to one or more (typically aplurality of) output waveguides. For example, inducing phase shifts inone or more waveguides using the phase shifters 504 changes thedistribution of light in the output waveguides.

FIG. 5B illustrates an example optical device, which corresponds to themulti-channel optical coupler 502-1 or 502-2 shown in FIG. 5A.

The optical device includes a first plurality of optical waveguidesformed in a first layer of material (e.g., waveguides represented bysolid lines in FIG. 5B) and a second plurality of optical waveguidesformed in a second layer of material that is distinct and separate fromthe first layer of material (e.g., waveguides represented by dashedlines in FIG. 5B). The second layer of material and the first layer ofmaterial are located at different heights on a substrate.

At least one optical waveguide of the first plurality of opticalwaveguides is coupled with an optical waveguide of the second pluralityof optical waveguides with any multi-mode optical coupler describedherein (e.g., the optical coupler 100 shown in FIGS. 1A-1G, the opticalcoupler 150 shown in FIG. 2 , etc.). For example, the optical deviceshown in FIG. 5B includes four optical couplers 518, 520, 522, and 524,each of which can have the structure of the optical coupler 100 shown inFIGS. 1A-1G or an analogous twisted configuration in which the twowaveguides cross each other as shown in FIG. 5B. Similar to the opticalcoupler 100 shown in FIGS. 1A-1G, each optical coupler has a couplingregion in which two waveguides propagate in parallel. Although the twowaveguides are illustrated in FIG. 5B as being offset from each other inthe coupling region, the two waveguides may be positioned directly aboveand below each other in the coupling region without offset as shown inFIG. 1A. In some embodiments, one or more of the optical couplers 518,520, 522, and 524 are configured to have a coupling efficiency ofapproximately 50% between the two waveguides (e.g., a couplingefficiency between 49% and 51%, a coupling efficiency between 49.9% and50.1%, a coupling efficiency between 49.99% and 50.01%, and a couplingefficiency of 50%, etc.). For example, the length of the two waveguides,the refractive indices of the two waveguides, the widths and heights ofthe two waveguides, the refractive index of the material located betweentwo waveguides, and the distance between the two waveguides are selectedto provide the coupling efficiency of 50% between the two waveguides.This allows the optical coupler to operate like a 50/50 beam splitter.

In addition, the optical device shown in FIG. 5B can include twointer-layer optical couplers 514 and 516, each of which has thestructure of the inter-layer optical coupler 300 shown in FIG. 3 . Theoptical coupler 514 allows transfer of light propagating in a waveguideon the first layer of material to a waveguide on the second layer ofmaterial, and the optical coupler 516 allows transfer of lightpropagating in a waveguide on the second layer of material to awaveguide on the first layer of material. Alternatively, the opticalcoupler 100 shown in FIG. 1 , configured for 100% coupling efficiency,may be used as the optical coupler 514 or the optical coupler 516.

Furthermore, the optical device shown in FIG. 5B includes a non-couplingwaveguide crossing region 526. In some implementations, the twowaveguides cross each other without having a parallel coupling regionpresent at the crossing in the non-coupling waveguide crossing region526 (e.g., the waveguides can be two straight waveguides that cross eachother at a nearly 90-degree angle).

The optical couplers 514 and 516 allows optical waveguides located in atleast two different layers to be used in the multi-channel opticalcoupler 502-1 or 502-2, which, in turn, enables a compact multi-channeloptical coupler. In addition, the use of multi-mode waveguides asdescribed above in reference to FIGS. 1-2 provides for a lower lossmulti-channel optical coupler as compared to implementations that relyon single mode waveguides only.

Although some of the drawings illustrate a number of logical stages in aparticular order, stages which are not order dependent may be reorderedand other stages may be combined or broken out. While some reordering orother groupings are specifically mentioned, others will be apparent tothose of ordinary skill in the art, so the ordering and groupingspresented herein are not an exhaustive list of alternatives. Moreover,it should be recognized that the stages could be implemented inhardware, firmware, software or any combination thereof.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit the scope of the claims to the precise forms disclosed. Manymodifications and variations are possible in view of the aboveteachings. The embodiments were chosen in order to best explain theprinciples underlying the claims and their practical applications, tothereby enable others skilled in the art to best use the embodimentswith various modifications as are suited to the particular usescontemplated.

What is claimed is:
 1. A generalized Mach-Zehnder interferometer,comprising: a first multi-channel optical coupler that includes four ormore output ports; a second multi-channel optical coupler that includesfour or more input ports; four or more optical waveguides, including: afirst optical waveguide of the four or more optical waveguides that isconnected to a first output port of the four or more output ports and afirst input port of the four or more input ports; and a second opticalwaveguide of the four or more optical waveguides that is connected to asecond output port of the four or more output ports and a second inputport of the four or more input ports; and one or more phase shifterscoupled with at least a subset of the four or more optical waveguides,wherein: at least one of the first multi-channel optical coupler or thesecond multi-channel optical coupler includes two or more multi-modeoptical couplers, including a first multi-mode optical coupler thatincludes: a first waveguide including a first multi-mode waveguidesection, the first waveguide being located in a first layer of material;and a second waveguide that is distinct and separate from the firstwaveguide, the second waveguide including a second multi-mode waveguidesection, the second waveguide being located in a second layer ofmaterial that is distinct and separate from the first layer of material,wherein the first multi-mode waveguide section is positioned adjacent tothe second multi-mode waveguide section; the first optical waveguideincludes a first portion in the first layer of material and a secondportion in the second layer of material and a first interlayer opticalcoupler coupling the first portion of the first optical waveguide to thesecond portion of the first optical waveguide; and the second opticalwaveguide includes a third portion in the second layer of material and afourth portion in the first layer of material and a second interlayeroptical coupler coupling the third portion of the second opticalwaveguide to the fourth portion of the second optical waveguide.
 2. Thegeneralized Mach-Zehnder interferometer of claim 1, wherein the firstmulti-mode optical coupler includes: the first multi-mode waveguidesection of the first waveguide of the first multi-mode optical couplerhas a cross-section characterized by a first height and a first widththat is greater than the first height; and the second multi-modewaveguide section of the second waveguide of the first multi-modeoptical coupler has a cross-section characterized by a second height anda second width that is greater than the second height, wherein the firstmulti-mode waveguide section is positioned adjacent to the secondmulti-mode waveguide section at least partially above or below thesecond multi-mode waveguide section so that light entering the firstmulti-mode waveguide section is coupled from the first multi-modewaveguide section to the second multi-mode waveguide section.
 3. Thegeneralized Mach-Zehnder interferometer of claim 2, wherein: the firstwidth is at least three times the first height; and the second width isat least three times the second height.
 4. The generalized Mach-Zehnderinterferometer of claim 1, wherein: the first multi-mode waveguidesection and the second multi-mode waveguide section are configured toallow light entering the first multi-mode waveguide section in afundamental mode is coupled from the first multi-mode waveguide sectionto the second multi-mode waveguide section while remaining in thefundamental mode.
 5. The generalized Mach-Zehnder interferometer ofclaim 1, wherein: the first waveguide of the first multi-mode opticalcoupler includes a third multi-mode waveguide section that is distinctfrom, and mutually exclusive to, the first multi-mode waveguide sectionso that light propagating in the third multi-mode waveguide sectionpropagates toward the first multi-mode waveguide section; and the secondwaveguide of the first multi-mode optical coupler includes a fourthmulti-mode waveguide section that is distinct from, and mutuallyexclusive to, the second multi-mode waveguide section so that lightpropagating in the fourth multi-mode waveguide section propagates towardthe second multi-mode waveguide section.
 6. The generalized Mach-Zehnderinterferometer of claim 5, wherein: the first waveguide of the firstmulti-mode optical coupler includes a fifth multi-mode waveguide sectionthat is coupled to the first multi-mode waveguide section on a first endand to the third multi-mode waveguide section on a second end that isopposite to the first end; and the second waveguide of the firstmulti-mode optical coupler includes a sixth multi-mode waveguide sectionthat is coupled to the second multi-mode waveguide section on a firstend and to the fourth multi-mode waveguide section on a second end thatis opposite to the first end, wherein at least one of the fifthmulti-mode waveguide section and the sixth multi-mode waveguide sectionis curved.
 7. The generalized Mach-Zehnder interferometer of claim 6,wherein: the first waveguide of the first multi-mode optical couplerincludes a seventh multi-mode waveguide section that is distinct from,and mutually exclusive to, the first multi-mode waveguide section sothat light propagating in the first multi-mode waveguide sectionpropagates toward the seventh multi-mode waveguide section; and thesecond waveguide of the first multi-mode optical coupler includes aneighth multi-mode waveguide section that is distinct from, and mutuallyexclusive to, the second multi-mode waveguide section so that lightpropagating in the second multi-mode waveguide section propagates towardthe eighth multi-mode waveguide section.
 8. The generalized Mach-Zehnderinterferometer of claim 7, wherein: the first waveguide of the firstmulti-mode optical coupler includes a ninth multi-mode waveguide sectionthat is coupled to the first multi-mode waveguide section on a first endand to the seventh multi-mode waveguide section on a second end that isopposite to the first end; and the second waveguide of the firstmulti-mode optical coupler includes a tenth multi-mode waveguide sectionthat is coupled to the second multi-mode waveguide section on a firstend and to the eighth multi-mode waveguide section on a second end thatis opposite to the first end, wherein at least one of the ninthmulti-mode waveguide section and the tenth multi-mode waveguide sectionis curved.
 9. The generalized Mach-Zehnder interferometer of claim 1,wherein: the first waveguide of the first multi-mode optical couplerincludes a first single-mode input waveguide section adiabaticallycoupled to the first multi-mode waveguide section so that the firstmulti-mode waveguide section receives light from the first single-modeinput waveguide section; and the second waveguide of the firstmulti-mode optical coupler includes a second single-mode input waveguidesection adiabatically coupled to the second multi-mode waveguide sectionso that the second multi-mode waveguide section receives light from thesecond single-mode input waveguide section.
 10. The generalizedMach-Zehnder interferometer of claim 9, wherein the first multi-modeoptical coupler of claim 9 includes: a first tapered waveguide section,in the first waveguide of the first multi-mode optical coupler,configured to enable the adiabatic coupling of the first single-modeinput waveguide section to the first multi-mode waveguide section; and asecond tapered waveguide section, in the second waveguide of the firstmulti-mode optical coupler, configured to enable the adiabatic couplingof the second single-mode input waveguide section to the secondmulti-mode waveguide section.
 11. The generalized Mach-Zehnderinterferometer of claim 10, wherein the first multi-mode optical couplerfurther includes in the first waveguide of the first multi-mode opticalcoupler: a first single-mode output waveguide section adiabaticallycoupled to the first multi-mode waveguide section so that the firstsingle-mode output waveguide section receives light from the firstmulti-mode waveguide section; and a third tapered waveguide sectionconfigured to enable the adiabatic coupling of the first multi-modewaveguide section to the first single-mode output waveguide section; andin the second waveguide of the first multi-mode optical coupler: asecond single-mode output waveguide section adiabatically coupled to thesecond multi-mode waveguide section so that the second single-modeoutput waveguide section receives light from the second multi-modewaveguide section; and a fourth tapered waveguide section configured toenable the adiabatic coupling of the second multi-mode waveguide sectionto the second single-mode output waveguide section.
 12. The generalizedMach-Zehnder interferometer of claim 1, wherein the first multi-modewaveguide section and the second multi-mode waveguide section areparallel to each other; and the first multi-mode waveguide section andthe second multi-mode waveguide section are separated from each other.13. The generalized Mach-Zehnder interferometer of claim 1, wherein: thetwo or more multi-mode optical couplers also include a second multi-modeoptical coupler that includes: a third waveguide including a thirdmulti-mode waveguide section, the third waveguide being located in thefirst layer of material; and a fourth waveguide that is distinct andseparate from the third waveguide, the fourth waveguide including afourth multi-mode waveguide section and being located in the secondlayer of material; the third multi-mode waveguide section is positionedadjacent to the fourth multi-mode waveguide section; and a portion ofthe second waveguide of the first multi-mode optical coupler ispositioned adjacent to a portion of the third waveguide for couplinglight from the second waveguide to the third waveguide.
 14. Thegeneralized Mach-Zehnder interferometer of claim 13, wherein: the two ormore multi-mode optical couplers also include a third multi-mode opticalcoupler and a fourth multi-mode optical coupler; the third multi-modeoptical coupler includes: a fifth waveguide including a fifth multi-modewaveguide section, the fifth waveguide being located in the first layerof material; and the fourth waveguide that is distinct and separate fromthe fifth waveguide, the fourth waveguide including a sixth multi-modewaveguide section that is different from the fourth multi-mode waveguidesection; the fifth multi-mode waveguide section is positioned adjacentto the sixth multi-mode waveguide section; the fourth multi-mode opticalcoupler includes: the first waveguide of the first multi-mode opticalcoupler including a seventh multi-mode waveguide section that isdifferent from the first multi-mode waveguide section; and a sixthwaveguide including an eighth multi-mode waveguide section, the sixthwaveguide being located in the second layer of material; the seventhmulti-mode waveguide section is positioned adjacent to the eighthmulti-mode waveguide section; and a portion of the fifth waveguide ispositioned adjacent to a portion of the sixth waveguide for couplinglight from the fifth waveguide to the sixth waveguide.
 15. Thegeneralized Mach-Zehnder interferometer of claim 1, wherein: the otherof the first multi-channel optical coupler and the second multi-channeloptical coupler includes two or more multi-mode optical couplers.